Complete proof of Eq.  is found in [1]}. When fusing other types of measurements the difference occurs in Eq. REF . For orientation and velocity measurements the Jacobian component is defined as:
\({\frac{\partial h}{\partial \textbf {x}_t} =\begin{bmatrix}0_3 & 0_3 & \text{I}_3 & 0_3 & 0_3 & 0_3 & 0_3 & \text{R}^T\lbrace \textbf {q}_{mv}\rbrace \end{bmatrix}}, \\\frac{\partial h}{\partial \textbf {x}_t} =\begin{bmatrix}0_3 & \text{I}_3 & 0_3 & 0_3 & 0_3 & 0_3 & 0_3 & 0_3\end{bmatrix},\) 
